If 1000!=3^n × m where m is an integer not divisible by 3 . then n=

Correct answer: (A) 498. Hint: E_3(1000!)= [1000/3 ]+ [1000/(3^2) ]+ [1000/(3^3) ]+ [1000/(3^4) ]+ [1000/(3^5) ]+ [1000/(3^6) ]=498

Q99 / 155 · WBJEE 2024 · Mathematics

If $1000!=3^n \times m$ where $m$ is an integer not divisible by 3 . then $n=$

Correct answer
A
498
B
298
C
398
D
98

Solution

Hint: $E_3(1000!)=\left[\frac{1000}{3}\right]+\left[\frac{1000}{3^2}\right]+\left[\frac{1000}{3^3}\right]+\left[\frac{1000}{3^4}\right]+\left[\frac{1000}{3^5}\right]+\left[\frac{1000}{3^6}\right]=498$

Hence, the correct answer is option: 'A'.

If $1000!=3^n \times m$ where $m$ is an integer not divisible by 3 . then $n=$

Solution

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